Rainman Posted September 11, 2012 Report Share Posted September 11, 2012 What is the maximum number of knights you can place on a regular chess board, so that each square has at most one knight threatening or occupying it? What is the minimum number of knights you can place on a regular chess board, so that each square has at least one knight threatening or occupying it? Quote Link to comment Share on other sites More sharing options...
0 Rob_Gandy Posted September 11, 2012 Report Share Posted September 11, 2012 (edited) Reveal hidden contents I can do it with 16 knights. I'm sure that's not the minimum, but it's a start. 4 squares of 4 with the knights in front of the 2nd and 3rd pawns. Edited September 11, 2012 by Rob_Gandy Quote Link to comment Share on other sites More sharing options...
0 Rainman Posted September 11, 2012 Author Report Share Posted September 11, 2012 That's a good start, but it's not the minimum. Quote Link to comment Share on other sites More sharing options...
0 curr3nt Posted September 12, 2012 Report Share Posted September 12, 2012 Reveal hidden contents 14 -------- --K--K-- --KKKK-- -------- --K--K-- -KK--KK- --K--K-- -------- Quote Link to comment Share on other sites More sharing options...
0 curr3nt Posted September 12, 2012 Report Share Posted September 12, 2012 Reveal hidden contents 12 -------- --K----- --KK-KK- -----K-- --K----- -KK-KK-- -----K-- -------- Quote Link to comment Share on other sites More sharing options...
0 Rainman Posted September 12, 2012 Author Report Share Posted September 12, 2012 (edited) Nice improvement, keep going Edit: scratch that, looks like you found the minimum Edited September 12, 2012 by Rainman Quote Link to comment Share on other sites More sharing options...
0 Rob_Gandy Posted September 12, 2012 Report Share Posted September 12, 2012 Reveal hidden contents I can do 12. k-----kk kk----k- -------- -------- -------- -------- -k----kk kk-----k Quote Link to comment Share on other sites More sharing options...
0 Rainman Posted September 12, 2012 Author Report Share Posted September 12, 2012 And that's the maximum, well done! Quote Link to comment Share on other sites More sharing options...
0 Rob_Gandy Posted September 13, 2012 Report Share Posted September 13, 2012 On 9/12/2012 at 7:39 PM, curr3nt said: Reveal hidden contents 12 -------- --K----- --KK-KK- -----K-- --K----- -KK-KK-- -----K-- -------- On 9/12/2012 at 8:17 PM, Rob_Gandy said: Reveal hidden contents I can do 12. k-----kk kk----k- -------- -------- -------- -------- -k----kk kk-----k Reveal hidden contents In both the maximum and minimum the knights are placed in the same basic pattern. That and they are the same number... Quote Link to comment Share on other sites More sharing options...
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Rainman
What is the maximum number of knights you can place on a regular chess board, so that each square has at most one knight threatening or occupying it?
What is the minimum number of knights you can place on a regular chess board, so that each square has at least one knight threatening or occupying it?
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